I can accurately name points, lines, planes, angles, rays and segments.
I can identify different types of angles including acute, obtuse, right, and straight.
I can classify triangles based on the angles and sides.
Parallel Lines:
I can name related angles when parallel lines are cut by a transversal. (Alt. Int. <s, Alt. Ext. <s, Corresponding<s, Same Side Int. <s).
I can use the fact that Alt. Int. <s, Alt. Ext. <s, Corresponding<s pairs are congruent both to solve unknown angles and prove lines parallel.
I can use the fact that Same Side int <s sum 180 degrees both to solve unknown angles and prove lines parallel.
Congruent Triangles:
- prove two triangles congruent by using SAS, SSS, ASA, HL, AAS congruence theorems.
- use the concept of corresponding parts of congruent triangles are congruent
- apply the concepts of congruent triangles to solve algebraic problems
- use the Isosceles triangle theorem and its converse to solve problems both algebraically and theoretically (proofs)
Indirect Proofs:
- use proof by contradiction to prove statements.
Types of Reasoning:
Deductive Reasoning:
- identify the hypothesis and conclusion of a conditional statement
- write an if-then statement based on a condtional statement
- write the converse, inverse, and contrapositive of a conditional statement
- determine the truth value of the if-then, converse, inverse, and contrapositive and provide counter- examples if they are false.
Inductive Reasoning:
- use patterns to predict future events or parts of the pattern
- look at 2 statements and be able to make a conclusion based on them or determine if there is no conclusion.
Triangles:
- I can find points of concurrency such as centroid, incenter, orthocenter and circumcenter.
- I can define median, altitude and midsegment and find the lengths of each.
- I can prove theorems about the interior and exterior angle measures of triangles.
- I can prove the base angles of a triangle are congruent.
-
Polygons:
- I can define, explain and find the measures of interior and exterior angles.
Quadrilaterals:
- name and identify the characteristics of the different types of quadrilaterals (parallelogram, rectangle, square, rhombus, trapezoid, iso. trapezoid, and kite).
- draw each type of quadrilateral correctly
- know and apply the different ways to prove a quadrilateral is a parallelogram
- solve equations using the properties of parallelograms.
- know the definition of a median of a trapezoid and know how to find it in a trapezoid.
Triangle Inequalities:
- be able to identify the longest to shortest sides of a triangle based on the angle measures
- be able to identify the the largest to smallest angles based on the side measurements
- use the SAS and SSS inequality theorems to identify relationships between angles and sides in a triangle.
Similar Triangles:
-I am able to find the missing sides in a set of similar triangles, given the lengths of at least three sides, in which two are corresponding.
Similar Figures:
Ratios and Proportions:
Right Triangles:
I can identify the hypotenuse.
I can find missing angle measures using the Triangle Angle Sum Theorem.
I can determine whether or not a triangle is right, obtuse or acute using the Pythagorean Inequalities.
I can determine missing lengths in a right triangle using the Pythagorean Theorem.
I can define the basic trig ratios in right triangles: sine, cosine and tangent.
I can find missing angle measure and side lengths in a right triangle using sine, cosine, and tangent.
I can apply the facts of right triangles to real-life situations in a way that helps me to determine missing measurements.
I can use scale drawings and trig to solve problems that include unknown distances and angle measures.
Circles:
Find arc lengths and areas of sectors of circles.
Determine the measures of central and inscribed angles and their associated major and minor arcs.
I can find the lengths of chords, radii and diameters within the same circle.
Constructions:
Area:
I can identify the base and height of a rectangle. I can use the base and height correctly to find the area of a rectangle using . I can identify the base and width of a triangle. I can use the base and width correctly to find the area of a triangle using . I can identify the bases and height of a trapezoid. I can use the bases and height correctly to find the area of a trapezoid using . I can identify the apothem, radius, and perimeter of a regular polygon. I can use right triangle trigonometry, and special right triangles to find missing radii, apothems and perimeter. I can use the apothem, radius, and perimeter correctly to find the area of a regular polygon using .
Surface Area and Volume:
Use the ratio of lengths in similar 2-D or 3-D abjects to find the ratio of their areas or volumes.
Derive a formula for the surface area of a cone as a function of its slant height and the circumference of its base.
Coordinate Geometry:
I can analyze 2-D figures in a coordinate plane using slope and distance to classify a polygon.
Transformations:
I can graph a translation, rotation, dilation and reflection with and without formulas.
I can graph compound transformations.
I can determine coordinate results of transformations using formulas or by graphing.
I can represent transformations within a coordinate system using vectors and matrices.
I can identify the reflection and rotation symmetries of 2-D and 3-D figures.
I can develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments.
Students should be able to:
General Geometric Knowledge:
I can accurately name points, lines, planes, angles, rays and segments.
I can identify different types of angles including acute, obtuse, right, and straight.
I can classify triangles based on the angles and sides.
Parallel Lines:
I can name related angles when parallel lines are cut by a transversal. (Alt. Int. <s, Alt. Ext. <s, Corresponding<s, Same Side Int. <s).
I can use the fact that Alt. Int. <s, Alt. Ext. <s, Corresponding<s pairs are congruent both to solve unknown angles and prove lines parallel.
I can use the fact that Same Side int <s sum 180 degrees both to solve unknown angles and prove lines parallel.
Congruent Triangles:
- prove two triangles congruent by using SAS, SSS, ASA, HL, AAS congruence theorems.
- use the concept of corresponding parts of congruent triangles are congruent
- apply the concepts of congruent triangles to solve algebraic problems
- use the Isosceles triangle theorem and its converse to solve problems both algebraically and theoretically (proofs)
Indirect Proofs:
- use proof by contradiction to prove statements.
Types of Reasoning:
Deductive Reasoning:
- identify the hypothesis and conclusion of a conditional statement
- write an if-then statement based on a condtional statement
- write the converse, inverse, and contrapositive of a conditional statement
- determine the truth value of the if-then, converse, inverse, and contrapositive and provide counter- examples if they are false.
Inductive Reasoning:
- use patterns to predict future events or parts of the pattern
- look at 2 statements and be able to make a conclusion based on them or determine if there is no conclusion.
Triangles:
- I can find points of concurrency such as centroid, incenter, orthocenter and circumcenter.
- I can define median, altitude and midsegment and find the lengths of each.
- I can prove theorems about the interior and exterior angle measures of triangles.
- I can prove the base angles of a triangle are congruent.
-
Polygons:
- I can define, explain and find the measures of interior and exterior angles.
Quadrilaterals:
- name and identify the characteristics of the different types of quadrilaterals (parallelogram, rectangle, square, rhombus, trapezoid, iso. trapezoid, and kite).
- draw each type of quadrilateral correctly
- know and apply the different ways to prove a quadrilateral is a parallelogram
- solve equations using the properties of parallelograms.
- know the definition of a median of a trapezoid and know how to find it in a trapezoid.
Triangle Inequalities:
- be able to identify the longest to shortest sides of a triangle based on the angle measures
- be able to identify the the largest to smallest angles based on the side measurements
- use the SAS and SSS inequality theorems to identify relationships between angles and sides in a triangle.
Similar Triangles:
-I am able to find the missing sides in a set of similar triangles, given the lengths of at least three sides, in which two are corresponding.
Similar Figures:
Ratios and Proportions:
Right Triangles:
I can identify the hypotenuse.
I can find missing angle measures using the Triangle Angle Sum Theorem.
I can determine whether or not a triangle is right, obtuse or acute using the Pythagorean Inequalities.
I can determine missing lengths in a right triangle using the Pythagorean Theorem.
I can define the basic trig ratios in right triangles: sine, cosine and tangent.
I can find missing angle measure and side lengths in a right triangle using sine, cosine, and tangent.
I can apply the facts of right triangles to real-life situations in a way that helps me to determine missing measurements.
I can use scale drawings and trig to solve problems that include unknown distances and angle measures.
Circles:
Find arc lengths and areas of sectors of circles.
Determine the measures of central and inscribed angles and their associated major and minor arcs.
I can find the lengths of chords, radii and diameters within the same circle.
Constructions:
Area:
I can identify the base and height of a rectangle.
I can use the base and height correctly to find the area of a rectangle using .
I can identify the base and width of a triangle.
I can use the base and width correctly to find the area of a triangle using .
I can identify the bases and height of a trapezoid.
I can use the bases and height correctly to find the area of a trapezoid using .
I can identify the apothem, radius, and perimeter of a regular polygon.
I can use right triangle trigonometry, and special right triangles to find missing radii, apothems and perimeter.
I can use the apothem, radius, and perimeter correctly to find the area of a regular polygon using .
Surface Area and Volume:
Use the ratio of lengths in similar 2-D or 3-D abjects to find the ratio of their areas or volumes.
Derive a formula for the surface area of a cone as a function of its slant height and the circumference of its base.
Coordinate Geometry:
I can analyze 2-D figures in a coordinate plane using slope and distance to classify a polygon.
Transformations:
I can graph a translation, rotation, dilation and reflection with and without formulas.
I can graph compound transformations.
I can determine coordinate results of transformations using formulas or by graphing.
I can represent transformations within a coordinate system using vectors and matrices.
I can identify the reflection and rotation symmetries of 2-D and 3-D figures.
I can develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments.